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A DPhil project available with Heather Harrington and Helen Byrne, Mathematical Institute, University of Oxford and Xin Lu, Ludwig Institute for Cancer Research, Nuffield Department of Medicine, University of Oxford


The student will be supervised by Professors Heather Harrington, Helen Byrne and Xin Lu in collaboration with Mark Middleton, Eamonn Gaffney, Philip Maini and Mark Coles.

Harrington and Byrne are mathematicians, interested in mechanistic understanding of complex biomedical systems like cancer, and develop mathematical and data analysis approaches to study them. The Lu lab identifies molecular mechanisms that control cellular plasticity and suppress tumour growth


We are undertaking a mathematical study of data from a checkpoint-inhibitor immunotherapy cancer clinical trial. Deep phenotyping data from two cohorts are available from this clinical trial. When sample sizes are small and the data inherently complex (i.e. nonlinear relationships), standard machine learning approaches are not suitable. Thus, a new approach is needed to analyse and integrate data from deep phenotyping of small numbers of patients. The student will develop mechanistic models to study patient cohort dynamics and outcomes and also study the genomic data using data analysis techniques involving networks and/or higher-order network structures, and potentially topological data analysis approaches.


In this project, clinical trial data will be analysed. The student will be trained in mathematical modelling, data analysis, computing, genomics, as well as related immune and oncology topics.


  • Otter, N., Porter, M.A., Tillmann, U. et al. A roadmap for the computation of persistent homology. EPJ Data Sci. 6, 17 (2017).
  • Peña-Chilet, M., Esteban-Medina, M., Falco, M.M. et al. Using mechanistic models for the clinical interpretation of complex genomic variation. Sci Rep 9, 18937 (2019).